August Bournonville (21 August 1805 – 30 November 1879) was a Danish ballet master and choreographer. He was the son of Antoine Bournonville, a dancer and choreographer trained under the French choreographer, Jean Georges Noverre, and the nephew of Julie Alix de la Fay, née Bournonville, of the Royal Swedish Ballet.

Bournonville was born in Copenhagen, Denmark, where his father had settled. He trained with his father Antoine Bournonville as well he studied under the Italian choreographer Vincenzo Galeotti at the Royal Danish Ballet, Copenhagen, and in Paris, France, under French dancer Auguste Vestris. He initiated a unique style in ballet known as the Bournonville School.

Following studies in Paris as a young man, Bournonville became solo dancer at the Royal Ballet in Copenhagen. From 1830 to 1848 he was choreographer for the Royal Danish Ballet, for which he created more than 50 ballets admired for their exuberance, lightness and beauty. He created a style which, although influenced from the Paris ballet, is entirely his own. As a choreographer, he created a number of ballets with varied settings that range from Denmark to Italy, Russia to South America. A limited number of these works have survived.

Bournonville's work became known outside Denmark only after World War II. Since 1950, The Royal Ballet has several times made prolonged tours abroad, not the least to the United States, where they have performed his ballets.

Bournonville's best-known ballets are La Sylphide (1836), Napoli (1842), Le Conservatoire (1849), The Kermesse in Bruges (1851) and A Folk Tale (1854). Later major ballets include Valkyrien, Thrymskviden, Arcona and Fjedstuen.

Born in Copenhagen on 21 August 1805, Bournonville was the son of the French ballet master Antoine Bournonville, who had settled in Denmark, and Lovisa Sundberg, a Swede. At the age of eight, he entered the Royal Ballet School at the Court Theatre in Christiansborg Palace under the tutelage of his father and Vincenzo Galeotti, ballet master and principal choreographer of the Royal Danish Ballet from 1775 to 1816.

On 2 October 1813, Bournonville made his first stage appearance in a small part as the son of a Viking king in Galeotti's Lagertha, the first ballet on a Nordic theme. Less than a year later, he received his first personal applause for dancing a Hungarian solo at the Court Theatre. In addition to dance, Bournonville was a voracious reader, learned French at home, played the violin, sang in a boy soprano voice, and studied declamation with the actors Michael Rosing, Lindgreen, and Frydensdahl. His many talents were brought together on the Queen's birthday, 29 October 1817, when as a twelve-year-old he played the role of Adonia to royal acclaim in a music-drama, Solomon's Judgment and sang a romance, "The Mother with Her Drooping Wings".

Bournonville had five siblings. He was the only one in out of the children who showed any interest in dancing. He married Helena Fredrika Håkansson on 23 June 1830. They had seven children, including Charlotte who became an opera singer and actress. Both sons died as toddlers.